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            <td colspan="1" rowspan="1" style="vertical-align: top;"> <br>
            <h1 style="text-align: center;"><big><big><big><a
 name="quantum_computing_encryption_attacks"></a>Post-quantum computing
cryptography analysis<br>
            </big></big></big></h1>
            <br>
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                  <ul>
                    <li>
                      <p><a href="#decryption_with_quantum_computers">POST-QUANTUM
CRYPTANALYSIS OF PEAZIP ENCRYPTION METHODS<br>
                      </a></p>
                    </li>
                  </ul>
                  </td>
                  <td style="vertical-align: top; width: 128px;">
                  <h2><img
 alt="effects of quantum computing on encryption"
 title="How quantum computing affects PeaZip encryption"
 src="file-format/security.png" style="width: 96px; height: 96px;"
 align="right"></h2>
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            <td
 style="background-color: rgb(255, 255, 255); vertical-align: top;">
            <div style="text-align: left; color: rgb(0, 0, 0);">
            <h2><big><big><big><a
 name="decryption_with_quantum_computers"></a><a
 href="#quantum_computing_encryption_attacks">Post-quantum
cryptanalysis of PeaZip encryption methods</a></big></big><br>
            </big></h2>
            </div>
            <br>
Security of encryption and hashing algorithm rely on computational
unfeasibility of solving some classes of hard mathematical problems in
reasonable time and with finite / cost effective computation resources.<br>
Quantum computing, based on quantum bits (qbits) which can exist in
superpositions of states, provides breakthrough performances in
solving some classes of hard mathematical problems over classic
computing methods, based on binary digital electronic architecture;
the impact of this performance improvement must be carefully evaluated
to assess
security of existing cipher and hash functions in a scenario where
quantum computers will be available.<br>
            <table style="width: 100%; text-align: left;" border="0"
 cellpadding="24" cellspacing="0">
              <tbody>
                <tr>
                  <td
 style="vertical-align: top; text-align: right; width: 128px;">
                  <h2><span style="font-weight: bold;"><img
 title="Breaking classic encryption with quantum computers"
 alt="impact of quantum computing on cryptography"
 src="file-format/quotes.png" style="width: 32px; height: 32px;"></span></h2>
                  </td>
                  <td style="vertical-align: top; font-style: italic;">Under
current understandings, the impact of increasingly more powerful
quantum computers with increasingly larger number of qbits has very
different degrees of impact on feasibility to reduce / break security
of algorithms commonly employed in <span style="font-weight: bold;">symmetric-key</span>
or <span style="font-weight: bold;">public-key</span> cryptography.</td>
                  <td style="vertical-align: bottom; width: 128px;">
                  <h3><img
 title="Attacks to classic cryptography algorithms with quantum machines"
 alt="break encryption with quantum computing"
 src="file-format/quotes-inverse.png" style="width: 32px; height: 32px;"></h3>
                  </td>
                </tr>
              </tbody>
            </table>
            <span style="font-style: italic;"></span><br>
            <h3><big style="font-weight: bold;">Quantum
computing and symmetric-key encryption algorithms</big></h3>
            <br>
            <a name="symmetric-key_encryption_quantum_computing"></a>To
preserve data secrecy, symmetric-key cryptography rely on a shared
secret element (password / passphrase, keyfile, biometric data, or
combinations of more factors as in two-factor authentication) between
two or more parties. <br>
The need to share this element, needed by receiver for decryption, is
the main
disadvantage of (secret) symmetric-key cryptography solutions over
public-key cryptography solutions.<br>
PeaZip currently supports only <a href="encrypt-files.html">symmetic-key
encryption</a> mechanisms, using password / passphrase and optionally
two-factor authentication (password / passphrase + key file), which
under current understandings are quite
secure against attacks by
arbitrarily sized quantum computers.<br>
Grover's quantum algorithm is the best-possible known attack for most
of current generation symmetric encryption algorithms (and hash
functions), providing - for NP-complete problems - a quadratic speed-up
over a classic computing based brute-force search.<br>
            <table style="width: 100%; text-align: left;" border="0"
 cellpadding="24" cellspacing="0">
              <tbody>
                <tr>
                  <td
 style="vertical-align: top; text-align: right; width: 128px;">
                  <h2><span style="font-weight: bold;"><img
 title="Quantum computing attacks to symmetric-key encryption"
 alt="quantum computing attacks on encryption"
 src="file-format/quotes.png" style="width: 32px; height: 32px;"></span></h2>
                  </td>
                  <td style="vertical-align: top; font-style: italic;">Consequently,
as a general rule, doubling the size of a symmetric key
can
effectively make up for the increase of efficiency of <span
 style="font-weight: bold;">Grover's
algorithm</span> over classic brute-forcing, and defeat the purpose of
these attacks.</td>
                  <td style="vertical-align: bottom; width: 128px;">
                  <h3><img
 title="Grover's algorithm atack on classical symmetric-key encryption"
 alt="quantum computing and symmetric key cryptography"
 src="file-format/quotes-inverse.png" style="width: 32px; height: 32px;"></h3>
                  </td>
                </tr>
              </tbody>
            </table>
In example, under those premises
AES 256 bit could be considered equivalent in security (when
arbitrarily large quantum computers are available, using Grover
algorithm over the 256 bit key space) to AES 128 bit (for
classic computers, using classic computing brute-force over the 128 bit
key space).<br>
Same holds true for other symmetric key ciphers like DES, Blowfish,
Twofish, and Serpent.<br>
While a quadratic speed-up (providing a sufficiently powerful quantum
computer is available) is an huge performance improvement, it is
nowhere near a complete breakthrough as polynomial time solution
provided by Shor's algorithm is for public-key encryption systems, so
post-quantum symmetric
cryptography is thought to not need to differ significantly from the
current generation.<br>
            <a name="grover_algorithm_attack"></a>Learn more: <a
 href="https://en.wikipedia.org/wiki/Grover%27s_algorithm">Grover's
algorithm<img title="Grover's quantum algorithm"
 alt="breaking symmetric key encryption" src="free-rar/extractor.png"
 style="border: 0px solid ; width: 12px; height: 10px;"><br>
            </a> <br>
            <br>
            <h3><big style="font-weight: bold;">Quantum
computing and public-key encryption algorithms</big></h3>
            <br>
            <a name="public-key_encryption_quantum_computing"></a>Public-key
encryption systems are currently extremely popular, as they
simplify key exchange task: anyone can encrypt a message using a public
key released by a receiver, but only receiver's private key can decrypt
messages protected by its public key.<br>
Unfortunately, most ones of currently popular public-key algorithms are
susceptible of being efficiently broken by a large enough quantum
computer.<br>
            <table style="width: 100%; text-align: left;" border="0"
 cellpadding="24" cellspacing="0">
              <tbody>
                <tr>
                  <td
 style="vertical-align: top; text-align: right; width: 128px;">
                  <h2><span style="font-weight: bold;"><img
 title="Quantum computing attacks to public-key encryption"
 alt="shor algorithm attack" src="file-format/quotes.png"
 style="width: 32px; height: 32px;"></span></h2>
                  </td>
                  <td style="vertical-align: top; font-style: italic;"><span
 style="font-weight: bold;">Shor's quantum algorithm</span> runs in
polynomial time to solve hard
mathematical problems used in most common public-key encryption
(integer
factorization problem, discrete logarithm problem, elliptic-curve
discrete logarithm problem), rather than in exponential or
sub-exponential time as the best, most efficient classic algorithms.</td>
                  <td style="vertical-align: bottom; width: 128px;">
                  <h3><img
 title="Shor's quantum algorithm attack to classic public-key encryption"
 alt="break publick-key with quantum computing"
 src="file-format/quotes-inverse.png" style="width: 32px; height: 32px;"></h3>
                  </td>
                </tr>
              </tbody>
            </table>
Experimenting public-key algorithms relying on problems not efficiently
simplified by Shor's algorithm or other quantum algorithms, being both
reasonably safe under classic computing and quantum computing -based
attacks, is currently an active research topic in cryptography.<br>
            <span style="font-style: italic;">PeaZip currently does not
support public-key encryption methods, only
symmetric (secret) -key encryption - keys (passwords, keyfiles) needs
to be privately, securely shared with receiver for decryption to take
place.</span><br>
            <a name="shor_algorithm_attack"></a>Learn more: <a
 href="https://en.wikipedia.org/wiki/Shor%27s_algorithm">Shor's
algorithm<img title="Shor's quantum algorithm"
 alt="breaking public key encryption" src="free-rar/extractor.png"
 style="border: 0px solid ; width: 12px; height: 10px;"></a>
.<br>
            <table style="width: 100%; text-align: left;" border="0"
 cellpadding="24" cellspacing="0">
              <tbody>
                <tr>
                  <td
 style="text-align: right; vertical-align: middle; width: 64px;">
                  <h3><span style="font-weight: bold;"><img
 title="What is quantum cryptography"
 alt="quantum cryptography security" src="file-format/information.png"
 style="width: 48px; height: 48px;"><br>
                  </span></h3>
                  </td>
                  <td
 style="font-style: italic; vertical-align: middle;"><big><a
 name="what_is_quantum_cryptography"></a>Please note <a
 href="https://en.wikipedia.org/wiki/Quantum_cryptography">quantum
cryptography</a></big><a
 href="https://en.wikipedia.org/wiki/Quantum_cryptography"><img
 alt="quantum cryptography" src="free-rar/extractor.png"
 style="border: 0px solid ; width: 12px; height: 10px;"></a><big> is a
separate topic, studying <span style="font-weight: bold;">how to
apply quantum phenomena to cryptography</span> in order to achieve
secrecy and detect
eavesdropping, rather than analyzing <span style="font-weight: bold;">how
quantum computers
characteristics affects safety</span> (in terms of computational
feasibility
of attacks or brute-forcing) of encryption / hashing algorithms - the
topic discussed in this page and properly named <a
 href="https://en.wikipedia.org/wiki/Post-quantum_cryptography">post-quantum
cryptography</a></big><a
 href="https://en.wikipedia.org/wiki/Post-quantum_cryptography"><img
 alt="post-quantum cryptography" src="free-rar/extractor.png"
 style="border: 0px solid ; width: 12px; height: 10px;"></a></td>
                </tr>
              </tbody>
            </table>
Read more about symmetic-key encryption algorithms supported by PeaZip:
Rijndael/<a target="_blank"
 href="http://en.wikipedia.org/wiki/Advanced_Encryption_Standard">AES<img
 src="free-rar/extractor.png" alt="aes256"
 title="symmetic-key AES encryption"
 style="border: 0px solid ; width: 12px; height: 10px;"></a>
(implemented as AES128 and AES256 in 7Z, ARC, PEA, and ZIP standards),
and <a target="_blank" href="https://www.schneier.com/twofish.html">Twofish<img
 title="Twofish cipher" alt="twofish 256 bit"
 src="free-rar/extractor.png"
 style="border: 0px solid ; width: 12px; height: 10px;"></a> and <a
 target="_blank"
 href="http://en.wikipedia.org/wiki/Serpent_%28cipher%29">Serpent<img
 title="Serpent cipher" alt="Serpent 256 bit"
 src="free-rar/extractor.png"
 style="border: 0px solid ; width: 12px; height: 10px;"></a> ciphers
(implemented for ARC and PEA standards).<br>
Read more about <a target="_blank"
 href="http://en.wikipedia.org/wiki/Cryptographic_hash_function">cryptographically
secure hash function<img alt="cryptographically secure hash algorithms"
 title="Non-invertible hash function" src="free-rar/extractor.png"
 style="border: 0px solid ; width: 12px; height: 10px;"></a><span
 style="background-color: rgb(255, 238, 221);"></span><br>
            </td>
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            <h3><a href="peazip-help-faq.html">FAQ</a>
&gt; Security &gt; Post-quantum computing
cryptanalysis</h3>
            <br>
Topics and search suggestions about effects of quantum computing on
PeaZip cryptography, security of AES, Twofish, Serpent algorithms,
impact of quantum-based attacks to try to break symmetric-key and
public-key encryption algorithms:<br>
            <table style="width: 100%; text-align: left;" border="0"
 cellpadding="6" cellspacing="0">
              <tbody>
                <tr>
                  <td
 style="vertical-align: top; width: 25%; font-style: italic;"> breaking
symmetic-key encryption with quantum
computing,<br>
break NP-complete problems,<br>
quadratic improvement,<br>
impact of quantum computing,<br>
quantum encryption attacks,<br>
Grover's algorithm attack,<br>
how encryption software works<br>
breaking cryptography,<br>
what is quantum cryptography,<br>
                  </td>
                  <td
 style="vertical-align: top; width: 25%; font-style: italic;"> breaking
public-key encryption with quantum
computing,<br>
polynomial time,<br>
Shor's algorithm attack,<br>
post-quantum cryptanalysis,<br>
break cryptographic software,<br>
attacking cryptography,<br>
impact of quantum computing attacks on encryption,<br>
how quantum cryptography works, </td>
                  <td
 style="vertical-align: top; width: 25%; font-style: italic;"> quantum
computing,<br>
aes256 algorithm,<br>
quantum encryption,<br>
exponential time solution,<br>
brute forcing,<br>
attack file encryption,<br>
break encryption algorithm,<br>
impact of quantum computers on cryptography,<br>
classic cryptography,<br>
                  </td>
                  <td
 style="vertical-align: top; width: 25%; font-style: italic;">NP-hard
problem,<br>
breaking encryption with quantum computers,<br>
decrypt with quantum machine,<br>
encryption security,<br>
attack encryption algorithm,<br>
break encryption with quantum machines,<br>
quantum cryptanalysis,<br>
classic vs quantum encryption<br>
                  </td>
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            <td style="vertical-align: top;">Tag Cloud<br>
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